Performance Measurement with Factor Models

Abstract

Identifying an appropriate benchmark is an essential step in assessing a manager's performance. In the prospectus or fund advertising materials, a benchmark for the fund is typically identified, and the performance of the fund relative to that benchmark is given. The issue of concern is whether or not the benchmark provided has a similar risk profile to the fund. Excerpt UVA-F-1673 Rev. Nov. 27, 2012 PERFORMANCE MEASUREMENT WITH FACTOR MODELS Identifying an appropriate benchmark is an essential step in assessing a manager's performance. In the prospectus or fund advertising materials, a benchmark for the fund is typically identified, and the performance of the fund relative to that benchmark is given. The issue of concern is whether or not the benchmark provided has a similar risk profile to the fund. Factor models, such as the Capital Asset Pricing Model (CAPM), generate a benchmark return for each fund based on its beta or systematic risk. Specifically, the expected return for a fund according to the CAPM (which I refer to below as RFundCAPMBenchmark) is given by Equation 1: RFundCAPMBenchmark Rrisk-free Fund(RMKT – Rrisk-free). (1) The beta of the fund is estimated by calculating the slope of the regression line of the excess return of the fund (RFund – Rrisk-free) on the excess return of the market (RMKT – Rrisk-free). Using this estimate of beta and the average returns of the market portfolio and the risk-free asset, we can compute the expected return of the fund, given the systematic risk taken by the manager. The value added by the manager or alpha is the difference between the total return on the fund for the period (RFund) and the benchmark return for the fund as determined by the CAPM formula (RFundCAPMBenchmark) given in Equation 2: . . .